The problem of selecting regression procedures indexed by tuning parameters is of course encountered in more general regression settings, and here cross-validation is typically the method of choice. One of the appeals of cross-validation is its inherently model-free nature which confers a certain robustness. It has been shown to be very successful empirically in non-parametric and high-dimensional regression settings and theoretical guarantees have provided additional support for its usage [1]}, [2]}, [3]}, [4]}, [5]}.
